Problem: If $x \diamond y = 3x-y$ and $x \boxdot y = x+6y$, find $(5 \boxdot -1) \diamond -3$.
First, find $5 \boxdot -1$ $ 5 \boxdot -1 = 5+(6)(-1)$ $ \hphantom{5 \boxdot -1} = -1$ Now, find $-1 \diamond -3$ $ -1 \diamond -3 = (3)(-1)-(-3)$ $ \hphantom{-1 \diamond -3} = 0$.